We investigate the significance of borrowing constraints in the market for consumer loans. Using data from the Consumer Expenditure Survey on auto loan contracts we estimate the elasticities of loan demand with respect to interest rate and maturity. We find that, with the exception of high income households, consumers are very responsive to maturity and less responsive to interest rate changes. Both elasticities vary with household income, with the maturity elasticity decreasing and the interest rate elasticity increasing with income. We argue that these results are consistent with the presence of binding credit constraints in the auto loan market.